An atomic force microscope (AFM) captures an image by scanning a mechanical probe tip across a surface of a sample. The probe tip senses molecular forces or friction between the probe tip and the sample. This sensing can be performed in different ways according to different AFM modes. For example, in a contact mode, the probe tip is mounted on a cantilever that is deflected in response to the forces between the probe tip and the sample. This deflection is measured in order to translate the detected forces into a representation of the sample's surface features.
As the probe tip is scanned across the sample, it may require height adjustment in order to accurately track the surface topology. In general, the probe tip should be maintained close enough to the surface for accurate sensing, but not so close that the force between the tip and sample becomes large enough to damage the probe tip and the sample.
The height of the probe tip is adjusted by a controller having a feedback loop. The controller outputs a control signal to an actuator to move the probe tip up or down by a desired amount, and it receives a feedback signal through the feedback loop to determine any necessary adjustments to the control signal. Components located between the control signal and the feedback loop are referred to collectively as the physical system of the AFM. The feedback signal can indicate, for instance, a difference between the desired movement of the probe tip and actual movement of the probe tip. It can also indicate interactions between the probe tip and the sample.
To safely image a surface, the controller must be able to adjust the probe tip height in a timely and accurate manner as the probe tip is scanned along the sample surface. Otherwise, the probe tip may crash into the sample surface before the controller can make required adjustments. Consequently, a safe scanning speed of the probe tip is limited by the bandwidth of the controller feedback loop.
In many commercial AFM controllers, the feedback loop uses a proportional-integral (PI) filter or a proportional-integral derivative (PID) filter to update the control signal. Due to the simplicity of these filters, however, the feedback loop is unable to correct for higher order vibrational resonances that may affect the height of the probe tip. This inability to correct for higher order resonances means that the probe tip must be moved at a slower rate to provide stable operation. Moreover, most AFMs require a user to tune the parameters of the feedback loop, but most users cannot properly configure parameters required to correct for higher order resonances.
Academic control theorists have designed more sophisticated AFM controllers to increase the feedback bandwidth of the AFM, but these AFM controllers have significant weaknesses as well. These AFM controllers are typically designed by constructing an analytical model of an AFM system in a process referred to as system identification, and then generating a formula for an AFM controller that will satisfy some design goal with respect to the modeled AFM system. For example, an analytical model of an AFM system can be constructed by measuring the frequency response of the AFM system and then generating an equation that captures all of the complex-valued poles and zeros of the measured system. A formula for an AFM controller can then be generated based on the AFM system equation.
One weakness of academic-designed AFM controllers is that system identification is imprecise, so it produces a flawed analytical model of an AFM system. This can result in a theoretically optimal controller that performs poorly in practice. Another weakness of academically-designed AFM controllers is that the tools to perform system identification and subsequent controller design tend to fail for systems with many (possibly weakly damped) poles and zeros and with time delays, which is typical for AFMs.
Due to the above shortcomings of commercially available and academically-designed AFM controllers, most existing AFM controllers are designed with a great deal of human interaction and verification. In other words, there are no automatic methods for creating sophisticated and stable AFM controllers.
What is needed, therefore, are automatic methods for designing AFM controllers that are more sophisticated than traditional PI or PID based AFM controllers.